scholarly journals Mathematical Thinking Styles—The Advantage of Analytic Thinkers When Learning Mathematics

2021 ◽  
Vol 11 (6) ◽  
pp. 289
Author(s):  
Jaime Huincahue ◽  
Rita Borromeo-Ferri ◽  
Pamela Reyes-Santander ◽  
Viviana Garrido-Véliz
Keyword(s):  
Mathematical Thinking ◽  
Quantitative Approach ◽  
Mathematical Tasks ◽  
Thinking Styles ◽  
Mathematical Performance ◽  
Test Instrument ◽  
Analytical Thinking ◽  
Learning Mathematics ◽  
Valid Test ◽  
Insight Into

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.

scholarly journals How To Learn To Understand Mathematics?

2017 ◽  
Vol 10 (2) ◽  
pp. 114
Author(s):  
Raymond Duval
Keyword(s):  
Mathematics Education ◽  
Cognitive Factors ◽  
Mathematical Tasks ◽  
Education For All ◽  
Teaching Mathematics ◽  
Mathematical Activity ◽  
Crucial Issue ◽  
Semiotic Representations ◽  
Learning Mathematics ◽  
Insight Into

The cognitive core process of mathematical activity is the recognition of a same object in two semiotic representations whose respective contents have nothing in common with each other. It is also the recurrent and insuperable difficulty of comprehension in learning mathematics and the main impediment to solving problems for most students. The theory of registers provides a cognitive analysis of the way of working and thinking in mathematics. It highlights the key cognitive factors to be taken into account in Mathematics Education for all students up to the age of 16. To give an insight into the theory this paper focuses on two topics. How to introduce letters and elementary algebra? How to learn to solve problems in mathematics? And to avoid the confusion of words arising in Mathematics Education whenever we talk about « theories », we shallshow how to analyze in terms of registers the mathematical tasks related to these two topics. This allow us to identify the cognitive thresholds to be crossed to understand and to solve problems in mathematics. Analyzing mathematical activity in terms of registers is quite different from the prevailing mathematical view. This concerns the hidden face of mathematical activity and not its exposed face. We are broaching here the crucial issue about teaching mathematics to all students up to the age of 16. What should be its objectives and priority areas?Keywords: Register. Transformation of Semiotic Representation. Conversion. Treatment. Discursive operation.

GEOGEBRA APPLICATION AS THE DEVELOPMENT OF LINEAR PROGRAM TEACHING MATERIALS IN SMA KABUPATEN BURU

2021 ◽  
Author(s):  
HARZIKO
Keyword(s):  
Communication Skills ◽  
Research Method ◽  
Positive Response ◽  
Mathematics Learning ◽  
Mathematical Communication ◽  
Realistic Mathematics ◽  
Test Instrument ◽  
Learning Mathematics ◽  
Quasi Experimental ◽  
Better Than

ABSTRACTThis research is motivated by the fact that the ability of mathematical communication in Indonesia is low. The models and approaches used in the learning process are one of the supporting factors for learning mathematics in the classroom. This study aimed to analyze SMA 1 Namlea students' mathematical communication skills with realistic mathematics learning assisted by GeoGebra. The research method used is quasi-experimental. WHO researched SMA Negeri 1 Namlea, Buru Regency. The analysis results show that the test instrument is valid and reliable to be used for pretest and posttest. The results showed that the mathematical communication of students who received realistic mathematics learning assisted by GeoGebra was better than students who received realistic mathematics learning without GeoGebra. The results also showed that there was a positive response from students towards learning realistic mathematics with GeoGebra.KEYWORDS: Realistic Mathematics, GeoGebra & Mathematical Communication

Mogućnosti primene istraživački zasnovane nastave (IN) u početnom matematičkom obrazovanju

2021 ◽  
Author(s):  
Dragana Glogovac ◽  
◽  
Marina Milošević ◽  
Bojan Lazić ◽  
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Teaching Mathematics ◽  
Teaching Process ◽  
Inquiry Based Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Key Competencies ◽  
Insight Into

Modern primary education, especially mathematics, requires constant innovation of teaching practice in order to modernize, rationalize, and efficiently the teaching process. Teaching mathematics should be experienced as a process that promotes learning with understanding, stimulates motivation, active learning, research, critical thinking, analysis, problem solving, drawing conclusions, exchange of experiences. The tendency to improve the quality of mathematics education has resulted in many studies pointing to the benefits of research-based mathematics (IN) teaching, known as inquiry-based learning (IBL), recognized as an essential way of organizing the teaching process to develop key competencies, abilities and skills in 21st century. Тhe aim of this paper is to see, based on a comprehensive theoretical analysis and the results of previous research. The created model of teaching mathematics based on research represents a useful framework for improving the quality of the process of teaching and learning mathematics, and empowers teachers in its application and affirmation, gaining insight into the way of organizing research learning.

scholarly journals The effects of CLIL on mathematical content learning: A longitudinal study

2016 ◽  
Vol 6 (2) ◽  
pp. 319-337 ◽  
Author(s):  
Jill Surmont ◽  
Esli Struys ◽  
Maurits Van Den Noort ◽  
Piet Van De Craen
Keyword(s):  
Foreign Language ◽  
Positive Impact ◽  
Traditional Education ◽  
Metalinguistic Awareness ◽  
First Year ◽  
Educational Approach ◽  
Content Learning ◽  
Mathematical Performance ◽  
Short Period ◽  
Insight Into

Previous research has shown that content and language integrated learning (CLIL), an educational approach that offers content courses through more than one educational language, increases metalinguistic awareness. This improved insight into language structures is supposed to extend beyond the linguistic domain. In the present study, the question whether pupils who learn in a CLIL environment outperform their traditionally schooled peers in mathematics is investigated. In total, 107 pupils entered the study. All participants were in the first year of secondary education at a school in Ostend, in Flanders, the Dutch-speaking part of Belgium. Thirty-five pupils followed CLIL education in a foreign language (French) and 72 followed traditional education that was given in the native language (Dutch). All participants were tested using a mathematical test at the beginning of the year, after three months, and after ten months. The first measurement of the mathematical scores showed that the two groups did not differ. In accordance with our hypothesis, the CLIL group scored higher than the non-CLIL group after ten months. Surprisingly, an effect was also found after three months. To conclude, CLIL appears to have a positive impact on the mathematical performance of pupils even after a short period of time.

It's a Home Run! Using Mathematical Discourse to Support the Learning of Statistics

2007 ◽  
Vol 101 (4) ◽  
pp. 250-256 ◽  
Author(s):  
Kathleen S. Himmelberger ◽  
Daniel L. Schwartz
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
National Council ◽  
Instructional Programs ◽  
Group Discussions ◽  
Good Communication ◽  
Mathematical Ideas ◽  
Positive Effects ◽  
Procedural Fluency ◽  
Learning Mathematics

The Standards developed by the National Council of Teachers of Mathematics (2000) state that instructional programs should enable all students to communicate mathematical ideas. The Standards indicate that good communication includes the ability to express organized and precise ideas as well as the ability to analyze and evaluate the mathematical thinking of others. Learning mathematics goes beyond procedural fluency; it also includes learning to discuss mathematical ideas. For this purpose, small groups have become a frequent configuration in the mathematics classroom. When combined with a suitable exercise, small-group discussions can have positive effects on mathematical understanding.

Beliefs and Their Influence on Mathematical Performance

1989 ◽  
Vol 82 (7) ◽  
pp. 502-505 ◽  
Author(s):  
Joe Garofalo
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Mathematical Tasks ◽  
Mathematical Task ◽  
Mathematical Content ◽  
Mathematical Performance ◽  
Mathematics Problems ◽  
Course Of Action ◽  
Mathematical Behavior ◽  
Research In Mathematics Education

Recent research in mathematics education has shown that success or failure in solving mathematics problems often depends on much more than the knowledge of requisite mathematical content. Knowing appropriate facts, algorithms, and procedures is not sufficient to guarantee success. Other factors, such as the decisions one makes and the strategies one uses in connect ion with the control and regulation of one's actions (e.g., deciding to analyze the conditions of a problem, planning a course of action, assessing progress), the emotions one fee ls while working on a mathematical task (e.g., anxiety, frustration, enjoyment), and the beliefs one holds relevant to performance on mathematical tasks, influence the direction and outcome of one's performance (Garofalo and Lester 1985; Schoenfe ld 1985; McLeod 1988). These other factors, although not explicitly addressed in typical mathematics instruction, are nonetheless important aspects of mathematical behavior.

Promoting Problem Solving across Geometry and Algebra by Using Technology

2005 ◽  
Vol 98 (9) ◽  
pp. 599-603
Author(s):  
A. Kursat Erbas ◽  
Sarah D. Ledford ◽  
Chandra Hawley Orrill ◽  
Drew Polly
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Teacher Support ◽  
Original Problem ◽  
Mathematical Thinking ◽  
School Students ◽  
And Algebra ◽  
Insight Into ◽  
Mathematics Problem

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. It is particularly effective when students are encouraged to explore a single mathematics problem with multiple technologies. Using technology allows students to be creative in their problem-solving techniques, look at data in a variety of ways, and see the viability of their answers, all of which may lead to a better understanding of mathematics. The vignette offered in this article provides insight into ways to solve open-ended problems by using multiple technologies. Although the series of events described is hypothetical, the original problem is familiar and the authors' collective experiences with such tasks and high school students indicates that the students are able to explore problems in ways that demonstrate and extend their mathematical thinking when they have appropriate teacher support.

Early Childhood Corner: ABCs of Early Mathematics Experiences

2005 ◽  
Vol 12 (4) ◽  
pp. 208-212
Author(s):  
Laurie E. Hansen
Keyword(s):  
Early Childhood ◽  
Mathematical Thinking ◽  
Early Age ◽  
Early Mathematics ◽  
Early Experiences ◽  
Learning Mathematics ◽  
Hands On ◽  
Everyday Experiences ◽  
Natural Way

Children begin to develop mathematical thinking long before they enter school. This acquisition occurs in a very natural way as children interact with the environment and their caregivers. Everyday experiences often lend themselves directly to learning mathematics. Planning meals, taking a bath, reading together, playing, and experiencing daily excursions are just a few examples of the daily opportunities children have to count, recognize shapes and numbers, and play with volume and measurement. Nurturing children's natural curiosity about, and aptitude in, mathematics at an early age is of utmost importance. A little encouragement can go a long way. Lozano and Medearis (1997) point out that young children's early experiences should be hands-on and meaningful.

scholarly journals As concepções de acadêmicos de Engenharia, no início do curso, sobre a Matemática e a aprendizagem Matemática

2020 ◽  
Vol 21 (3) ◽  
pp. 314-323
Author(s):  
Eliéverson Guerchi Gonzales ◽  
Kátia Guerchi Gonzales ◽  
José Matheus Pinheiro da Fonseca da Silva
Keyword(s):  
Linear Algebra ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Education Institution ◽  
Mathematical Concept ◽  
Private Higher Education ◽  
Analytical Geometry ◽  
Mato Grosso ◽  
Learning Mathematics ◽  
Mato Grosso Do Sul

ResumoA pesquisa teve como objetivos investigar e analisar as concepções de Matemática, da aprendizagem de Matemática e do pensamento matemático dos acadêmicos dos primeiros semestres dos cursos de Engenharia Elétrica, Engenharia da Computação e Engenharia Ambiental de uma instituição privada de Ensino Superior, localizada na cidade de Campo Grande, Mato Grosso do Sul, Brasil. Trata-se de uma pesquisa qualitativa realizada com os ingressantes do ano de 2018. Nesta pesquisa foram utilizados questionários, juntamente com entrevistas sob a luz da História Oral. Para análise, foram necessários dois movimentos: um no trabalho das narrativas produzidas pelas entrevistas e outro em relação aos questionários. As análises, a partir dos questionários, permitiram identificar, de modo geral, manifestações de concepção Matemáticas coesas predominante, como também, do pensamento Matemático especulativo. Quanto à concepção em relação à aprendizagem de Matemática, as manifestações foram equivalentes. Sobre as concepções dos estudantes na disciplina de Geometria Analítica e Álgebra Linear (GAAL), a concepção de aprendizagem de Matemática foi a instrumental, a concepção de Matemática se revelou coesa e o pensamento matemático permeou entre o investigativo e o exato. Nas entrevistas, tanto as concepções que se referem à Matemática, de maneira geral, quanto às concepções da disciplina de GAAL, foram as mesmas. Identificam-se as concepções de aprendizagem de Matemática relacional, a concepção de Matemática coesa e o pensamento Matemático especulativo. Palavras-chave: Concepções de Matemática. Geometria Analítica e Álgebra Linear Aprendizagem. AbstractThis paper investigates and analyzes mathematics conceptions, mathematics learning and mathematical thinking of the first semester students from Electrical Engineering, Computer Engineering and Environmental Engineering courses of a private Higher Education institution, located in the city of Campo Grande, Mato Grosso do Sul, Brazil. This is a qualitative research conducted with the freshmen of the year 2018. In this research, questionnaires were used, together with interviews in the light of Oral History. For the analysis, two approaches were necessary: first looking into the narratives produced by the interviews and a second one with associated questionnaires. The questionnaire analyzes allowed us to identify, in general, manifestations of predominant cohesive mathematical conceptions, as well as, of speculative mathematical thinking. As for the comprehension associated with learning mathematics, the manifestations were equivalent. Regarding the students' mathematical concept of Analytical Geometry and Linear Algebra (AGLA), the concept of learning mathematics was the instrumental one, and so the mathematics concept proved to be cohesive with investigative and exact mathematical thinking. In the interviews, both the concepts that refer to mathematics and the AGLA discipline were the same. Concepts of relational mathematics learning, the concept of cohesive mathematics and speculative mathematical thinking were identified. Keywords:. Mathematics Conceptions. Analytical Geometry and Linear Algebra Learning.

Sign in / Sign up

Export Citation Format

Share Document